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Math Help - Sequence proof

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    Sequence proof

    If you have a sequence a_n which is bounded below and a sequence b_n which is bounded below, show that a_n + b_n is bounded below. The definition of bounded below is a_n > -M.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by natester View Post
    If you have a sequence a_n which is bounded below and a sequence b_n which is bounded below, show that a_n + b_n is bounded below. The definition of bounded below is a_n > -M.
    your definition of being bounded below seems to be lacking. anyway, if that's what you are given, here is how we proceed. (i will write M instead of -M, 'cause that looks weird).

    so we have a_n > M and b_n > K for all n.

    thus, a_n + b_n > M + K for all n. so a_n + b_n is bounded below by M + K
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    That makes since to me, but how would I prove that the statement a_n + b_n > M + K is true?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by natester View Post
    That makes since to me, but how would I prove that the statement a_n + b_n > M + K is true?
    um, it's not really something you have to prove. unless you want to go down to some kind of axiomatic level of number theory, which i doubt. it is just common sense that if you diminish each term, the result will be smaller

    like since 2 > 1 and 3 > 1 it just makes sense that 2 + 3 > 1 + 1, because in place of two larger numbers, we put two smaller numbers, so the result must be smaller ...
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